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On contra-symmetry and MPT conditionality in fuzzy logic. (English) Zbl 1088.03025
The study of contra-positive symmetry of fuzzy implication operators was initiated by J. C. Fodor [Fuzzy Sets Syst. 69, No. 2, 141–156 (1995; Zbl 0845.03007)]. The present paper continues and extends this study to the investigation of \(N\)-contrapositive symmetry \((N: [0,1]\to [0,1]\) is an order-reversing involution) of fuzzy implication operators verifying either the Modus Ponens or the Modus Tollens principle. It is shown that in the fuzzy framework these principles are not longer equivalent, unless the discussed implication operator is contra-symmetrical, as happens with some \(S\)-implications. New types of contra-symmetrical fuzzy implication operators generalizing the so-called Dishkant arrows in orthomodular lattices are also introduced.

MSC:
03B52 Fuzzy logic; logic of vagueness
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